Preheat oven to 350°F. Cream butter, brown sugar, and granulated sugar until light and fluffy, 2 to 3 minutes. Add eggs one at a time, then vanilla, mixing well after each.

Whisk together flour, baking soda, and salt. Gradually add to wet mixture, mixing until just combined. Fold in chocolate chips.

Scoop dough into 8 equal portions. Flatten each into a disc. Place an Oreo in the center, wrap the dough around, and seal completely. Refrigerate shaped cookies for at least 30 minutes.

Place chilled dough balls 3 inches apart on a lined baking sheet. Bake 12 to 14 minutes until edges are golden and centers look slightly underdone.

Cool on the sheet for 5 minutes, then transfer to a wire rack. Serve warm.